Problem: Vanessa is 12 years older than Emily. Fourteen years ago, Vanessa was 4 times as old as Emily. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Vanessa and Emily. Let Vanessa's current age be $v$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $v = e + 12$ Fourteen years ago, Vanessa was $v - 14$ years old, and Emily was $e - 14$ years old. The information in the second sentence can be expressed in the following equation: $v - 14 = 4(e - 14)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = e + 12$ . Substituting this into our second equation, we get the equation: $(e + 12)$ $-$ $14 = 4(e - 14)$ which combines the information about $e$ from both of our original equations. Simplifying both sides of this equation, we get: $e - 2 = 4 e - 56$ Solving for $e$ , we get: $3 e = 54$ $e = 18$.